Two women required hospital treatment for the injuries they received, and the man was also injured.
The maximum penalty for the charge of wounding with the intent to injure is 14 years imprisonment.
The third charge relates to the stabbing of dog Honey, which has a maximum penalty of six months' imprisonment or a $25,000 fine.
The dog ran off at the time of the incident but was later found and returned to its owners.
Zembergs was remanded in custody until his next appearance which was today and his defence counsel Leo Lafferty made no further applications, he was further remanded in custody for a case review hearing on May 20.